Justify your reasoning.

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Presentation transcript:

Justify your reasoning. Equivalent Equations Justify your reasoning. Image from http://schools.iclipart.com

Write an equation that is true when… Examples: 3x = 0 5t – 4 = 1 -32y - 24 = -8 z(52) = 25π x = 0 t = 1 or -1 y = -0.5 z = π Image from http://schools.iclipart.com

Why would each of the following equations have the SAME solution set? (A solution set is the group of all answers to an equation.) 5x - 3 = 2(x + 2) and 5x - 3 = 2x + 4 The distributive property. 3x = 1 + x and 3x = x + 1 The commutative property. 12 = (1 + x) + 5 and 12 = 1 + (x + 5) The associative property. Image from http://schools.iclipart.com

Would each of the following equations have the same solution set Would each of the following equations have the same solution set? Why or why not? 3x = 1 + x and 3x + 500 = 1 + x + 500 Yes. The subtraction property of equality could subtract 500 from both sides of the 2nd equation. Then they would be equivalent. 3x = 1 + x and 9x = 3(x + 1) Yes. The division property of equality could divide 3 from both sides of the 2nd equation. Then they would be equivalent. Image from http://schools.iclipart.com

Write an equation that would be equivalent to… -6x - 4 = x – 9 What algebraic property did you use? Share your equation with a neighbor to verify that it is equivalent. 16x – 8 = 4x What algebraic property did you use? Share your equation with a neighbor to verify that it is equivalent. Image from http://schools.iclipart.com

The equation 2x + 4 = 6x – 2 is equivalent to all of the following The equation 2x + 4 = 6x – 2 is equivalent to all of the following. Which property was used to change the equation? Multiplication property (•-1) Subtraction property (-2x) Subtraction property (-2) Addition property (+x) Division property (÷2) Subtraction property (-5) -2x – 4 = -6x + 2 4 = 4x – 2 2x + 2 = 6x – 4 3x + 4 = 7x – 2 x + 2 = 3x – 1 2x – 1 = 6x - 7

Match up equations with the same solution Match up equations with the same solution. Explain how you know they had the same solution using properties. 2x – 3 = 5x + 7 2x + 3 = 5x – 7 10x – 8 = 6x + 10 2x – 2 = 5x – 12 4x – 6 = 10x + 14 5x – 4 = 3x + 5 A & E = Multiplication property (•2) B & D = Subtraction property (-5) C & F = Division property (÷2) Image from http://schools.iclipart.com